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Syllabus ( MATH 447 )


   Basic information
Course title: Tensor Analysis
Course code: MATH 447
Lecturer: Prof. Dr. Oğul ESEN
ECTS credits: 5
GTU credits: 3 (3+0+0)
Year, Semester: 4, Fall and Spring
Level of course: First Cycle (Undergraduate)
Type of course: Departmental Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: Math 113
Professional practice: No
Purpose of the course: Teach the basic concepts of tensor calculus and it’s applications in physics and applied mathematics.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Build up a solid background of tensor calculus.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    3. Ability to work in interdisciplinary research teams effectively.

    Method of assessment

    1. Term paper
  2. Use the basic concepts of applied mathematics

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    3. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Term paper
  3. The students learn the application of Tensors which are the most important tools for the concept of Invariance.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    3. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.

    Method of assessment

    1. Written exam
   Contents Up
Week 1: The concept of invariance, physical transformations and the concept of invariant equations.
Week 2: Translational and rotational transformations.
Week 3: Lorentz transformations and the broken invariance of Newton equation under Lorentz transformations.
Week 4: Scalar invariants under these transformations. The infinitesimal arc length and its basis situation for tensorel calculations.
Week 5: Vectors and their invariance principles. 2nd order and higher order tensors.
Week 6: Maxwell equations and their invariance under Lorentz transformations.
Week 7: Relativistic electrodynamics and its formalism.
Week 8: Midterm Exam and solutions
Week 9: Riemannian geometry and its principal tensors, Ricci, Riemann tensors
Week 10: Einstein field equations and general relativity as a tensorel theory.
Week 11: Various examples to the solutions of Einstein field equations.
Week 12: Main solution techniques and the analysis of general relativity.
Week 13: Lagrange theory of fields and writing invariant action functional. The application of tensors to physical sciences.
Week 14: Invariant field theories and their difference from coordinate based theories.
Week 15*: -
Week 16*: Final exam
Textbooks and materials: General Relativity, Robert M. Wald, The University of Chicago Press, 1984
A Short Course in General Relativity, J. Foster, J. D. Nightingale, Springer-Verlag, 1995
Recommended readings: Mathematical Methods for Physicists (Weber and Arfken)
Tensors, Differential Forms and Variational Principles (David Lovelock and Hanno Rund)
Tensor Analysis for Physicists (J. A. Schouten)
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 2 14
Practice, Recitation: 0 0
Homework: 0 0
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 1
Mid-term: 3 1
Personal studies for final exam: 10 4
Final exam: 3 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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